Question

Use Huygens’s principle to explain the formation of diffraction pattern due to a single slit illuminated by a monochromatic source of light.

Answer 1

Consider a parallel beam of monochromatic light is incident normally in a slit of width b as shown if figure. According to Huygens’s principle every point of slit acts as a source of secondary wavelets spreading in all directions. Screen is placed at a larger distance.

Consider a particular point P on the screen receives waves from all the secondary sources. All these waves start from different point of the slit and interface at point P to give

Point P₀ is at bisector plane of the slit. At P₀, all waves are traveling equal optical path. So are in phase the waves thus interface constructively with each other and maximum intensity is observed. As we move from P₀, the wave arrives with different phase and intensity is changed. Intensity at point P is given by

`I = I_0  (sin^2α)/alpha`

where `alpha = pi/lambda b sin theta`

For central maxima α = 0 thus,

I = I₀